Macrorealism is a classical world view asserting that the properties of macro-objects exist independently and irrespective of observation. One practical approach to test this view in quantum theory is to observe the quantum coherence for a macro-object in an interference experiment. An elegant and conceptually appealing approach for testing the notion of macrorealism in quantum theory is through the violation of Leggett-Garg inequality. However, a conclusive Leggett-Garg test hinges on how the noninvasive measurability criteria are guaranteed in an experiment and remains a debated issue to date. In this work, we connect the practical and the conceptual approaches for testing the macrorealism through the weak value. We argue that whenever a quantum effect is observed in an interference experiment there is an existence of anomalous weak value. Further, we demonstrate that whenever such weak value exists, one obtains the violation of a Leggett-Garg inequality in any interference experiment. Since in a path-only interference experiment effectively no prior measurement is performed, the Leggett-Garg test of macrorealism presented here is without assuming the noninvasive measurability. We provide a rigorous discussion about the assumptions involved in the Leggett-Garg scenario and how our scheme fits into it. Further, we provide a simple argument about the macrorealistic understanding of our results by using the recently developed approach involving quasiprobability.
In the tests for macrorealism proposed by Leggett and Garg, the temporal correlation functions of a dichotomic variable
Q must be measured in a noninvasive way to rule out alternative classical explanations of Leggett-Garg inequality violations. Ideal negative measurements in which a null result is argued to be a noninvasive determination of the system's state are often used. From a quantum-mechanical perspective, such a measurement collapses the wave function and will therefore typically be found to be invasive under any experimental check. Here, a simple modified ideal negative measurement protocol is described for measuring the correlation functions, which is argued to be noninvasive from both classical and quantum perspectives and hence the noninvasiveness can then be checked experimentally, thereby permitting a quantitative measure of the degree of clumsiness of the measurement. It is also shown how this procedure may be extended to measure higher-order correlation functions, and a number of higher-order conditions for macrorealism are derived.
The Leggett-Garg inequality holds for any macrorealistic system that is being measured noninvasively. A violation of the inequality can signal that a system does not conform to our primal intuition about the physical world. Alternatively, a violation can simply indicate that a ``clumsy'' experimental technique led to invasive measurements. Here, we consider a recent Leggett-Garg test designed to try to rule out the mundane second possibility. We tailor this Leggett-Garg test to the IBM 5Q Quantum Experience system and find compelling evidence that qubit
Q2 of the system cannot be described by noninvasive macrorealism.